• 講演者 : Soma Purkait氏 (東京理科大学)
    • 題目 : Hecke algebra of $\DSL_2(\Q_p)$ and newforms of half-integral weight
    • 日時 : 平成29年4月27日(木)17:00 -- 18:00

The Hecke algebra of $\GL_2(\Q_p)$ with respect to Iwahori subgroup is well-known. We extend this to study genuine Hecke algebra of the double cover $\DSL_2(\Q_p)$ with respect to certain open compact subgroups. We translate certain elements of this Hecke algebra to obtain classical operators on the space of cusp forms of half-integral integral weight. We use these operators to indentify the ``minus space'' of level $4M$, $M$ odd and square-free. Our minus space is the counterpart of Kohnen's plus space in the sense that it is Hecke isomorphic to $S_{2k}^{\mathrm{new}}(2M)$. In an analogy with our work in the integral weight setting we show that the minus space is characterized as a common eigenspace of certain finite set of operators with given eigenvalues. This is a joint work with Prof. E. M. Baruch.

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Last-modified: 2017-04-12 (水) 10:57:12 (128d)